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Domain decomposition based parallel Howard’s algorithm

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  • Festa, Adriano

Abstract

The Howard’s algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A useful characteristic of the method is the superlinear convergence which, in presence of a finite number of controls, is reached in finite time. Performances of the method can be significantly improved using parallel computing. Building a parallel version of the method is not trivial because of the hyperbolic nature of the problem. In this paper we propose a parallel version of the Howard’s algorithm driven by an idea of domain decomposition. This permits to derive some important properties and to prove the convergence under standard assumptions. The good features of the algorithm are shown through some tests and examples.

Suggested Citation

  • Festa, Adriano, 2018. "Domain decomposition based parallel Howard’s algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 121-139.
    • Handle: RePEc:eee:matcom:v:147:y:2018:i:c:p:121-139
    DOI: 10.1016/j.matcom.2017.04.008
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    1. Manuel Santos & John Rust, "undated". "Convergence Properties of Policy Iteration," Working Papers 2133377, Department of Economics, W. P. Carey School of Business, Arizona State University.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    3. Martin L. Puterman & Shelby L. Brumelle, 1979. "On the Convergence of Policy Iteration in Stationary Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 60-69, February.
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    Cited by:

    1. Roberto Ferretti & Adriano Festa, 2019. "Optimal Route Planning for Sailing Boats: A Hybrid Formulation," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1015-1032, June.

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